2020/06/18 by Xinyue Cheng, Qiuhong Qu, Cheng, Xinyue +3
Mathematics · Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2006.10557
openalex publication_date 2020/06/18 · openalex created_date 2020/06/25 · openalex updated_date 2026/07/28
In this paper, we study navigation problems on conic Kropina manifolds. Let F(x, y) be a conic Kropina metric on an n-dimensional manifold M and V be a conformal vector field on (M, F) with F(x, - Vx)≤ 1. Let \widetildeF= \widetildeF (x,y) be the solution of the navigation problem with navigation data (F, V). We prove that \widetildeF must be either a Randers metric or a Kropina metric. Then we establish the relationships between some curvature properties of F and the corresponding properties of the new metric \widetildeF, which involve S-curvature, flag curvature and Ricci curvature.